Thoughts on the Theory of the Firm

One of the interesting questions in economics is why markets coordinate some forms of production but firms coordinate others. Or to put it more sharply, if centralized economic planning doesn’t work for countries, why does it work for firms?

In principle, it should be possible to coordinate production solely through market transactions among individuals. Everyone would be some combination of an independent contractor and a capital owner. The challenge of course would be establishing the necessarily fluid markets, not to mention all the time everyone would have to spend negotiating contracts for their labor and capital.

Thus the standard approach to explaining firms starts with the Transaction Cost theory (typically attributed to Coase). Whenever the cost of a market-based mechanism is higher than a firm-based mechanism, a firm will end up coordinating production. Of course, to anyone who has ever started a new firm or worked any length of time at a large one, this explanation is not terribly satisfying. How do you know the relative costs in the first place and then explain the apparently wasted resources at large companies? Newer theories have tried to do better, but none seem to tell the whole story. See here for an overview of the literature.

Another unsatisfying aspect of mainstream Theories of the Firm is that they don’t explain the observed interactions of firms with the macroeconomy very well. For example, firms don’t responsively lower existing salaries when the demand for labor goes down or the supply goes up. Firms also seem to forego internal price-based mechanisms that would allow them to respond more flexibly to macro shifts in cost and demand. Even more puzzling, there’s no good explanation of why and when some large firms grow dramatically while others die off. I’ve seen some attempts to address particular questions, but they seem like a patchwork rather than a coherent framework.

The always insightful Arnold Kling refers to a tweet from fellow GMU economist Garett Jones as one possible explanation: “Workers mostly build organizational capital, not final output”. Unfortunately, this is a tweet, not a theory. I was sort of playing around with the idea to see if I could get a decent theory out of it and I think I may have something. It ties together microeconomics, entrepreneurship, search theory, options theory, principal-agent theory, and group dynamics.

The basic idea is: firms don’t produce products; firms produce production functions. It seems obvious in retrospect, but a cursory search of the literature didn’t turn up anything similar. Someone has probably thought of this before. But perhaps I got lucky. So I’ll run with the ball for now.

What Is a Production Function?

In economics, a production function is an abstract model of how an economic actor turns inputs into outputs. Basically, it represents the formula or a recipe for a product. Typically, we write Q=f(X), where Q is a vector of output quantities, f is the production function, and X is a vector of input quantities. While “real” production functions have very specific outputs and inputs, economists often simplify the world by assuming each actor only produces one output, Goods, and there are a standard set of general inputs such as Labor, Capital, and Land. If we know the cost curves of Labor, Capital, and Land, we can calculate a cost curve for Goods and examine the tradeoffs and synergies among Labor, Capital, and Land.

Typically, economic theory defines a firm in terms of its production function. However, anyone who has ever founded a startup or worked in a large company should find this definition puzzling. When I’ve started companies, I could not even clearly define what our inputs and outputs would be, let alone the formula for turning the former into the latter. When I’ve interacted with big companies, I typically see a lot of people and groups who have nothing to do with turning inputs into outputs. For example, CTO, CIO, CFO, Corporate Development, Business Development, Product Management, Brand Management, and Market Research. In fact, when I think about the technology industry, the fraction of people actually involved in transforming of inputs to outputs, even if you count the relevant management hierarchy, seems pretty small.

So what is it that entrepreneurs and most of the of the people at large companies are actually doing? My hypothesis is that they are exploring alternative production functions: trying to figure out ways to improve existing businesses and explore opportunities for completely new businesses. Intuitively, this seems reasonable given my experience, but I’d never thought of how to formalize the concept.

Now some production functions are conceptually “near” current ones in that they represent small refinements to the manufacturing process or modest enhancement to existing products. Other production function are conceptually “far” from current ones in that they introduce radical new manufacturing technologies or generate revolutionary new products. I bet if you think about the people you’ve worked with, most of them are involved in figuring out how to produce things or what things to produce, rather than actually producing things. So they are producing production functions.

Production Function Space

The cool way to approach this kind of search problem is to posit a high-dimension space of all the alternatives with a structure that allows us to define the concepts of “near” and “far”. In this case we have production function space.

The challenge is that most points in this space are not economically viable. Some of them define products that nobody wants (e.g., Apple Newtons). Some of them define products that we can’t make at our current level of technology (e.g., flying cars). Some of them define products that we could make but whose demand curve never intersects its cost curve (e.g., diamond coated toothpicks).

Moreover, there are a lot of dependencies among points in production function space. So you can’t consider just one point in isolation; you have to consider configurations of points. Some Goods in one production function are Capital in another production function (e.g., Intel processors). In other cases, demand for some Goods exists only if there is also demand for other Goods (e.g., third party iPhone cases and Apple iPhones).

Most importantly, the goal is not just to find economically viable points. The goal is to find points that generate a lot of profit. Given that changes in technology and fashion cause these points to constantly shift relative to each other and the high dimensionality of the relationships among points, we have a rather complex optimization problem. I think of it as the potfolio optimization problem from finance, combined with the n-body problem from physics, combined with the protein folding problem from biology.

Given this level of complexity, we would expect that search strategies almost always use heuristics and trial-and-error rather than purely analytic optimization.

The Implications

In subsequent posts, I plan to analyze this hypothesis from several different angles. I also hope to come up with some predictions that someone could test. But I thought it would be useful to throw out some gross speculation right now to show how this insight crystallized my thinking and pique your interest in exploring further:

– The value of a firm is the present value of the profit stream from actual current production functions plus the option value of potential future production functions.

– Large firms tend to explore neighborhoods of production function space relatively near the surfaces defined by their current products.

– Startups tend to explore neighborhoods of production function space relatively distant from the surfaces defined by everyone else’s current products.

– Firms that have released successful new products are more valuable because this success implies greater skill in searching production functions space.

– Firms that have released successful new products are also more valuable because they then have a larger beachhead from which to explore greater regions of production function space in the future. Luck counts.

– Large firms acquire startups in part to increase their ability to search more distant regions of production function space.

– Due to network effects among colleagues and the uniqueness of each firm’s endowments, a given firm’s ability to search production function space is proportional to the number of employees it has and their length of service.

– It is harder to observe the true contribution of a particular employee to searching production function space than it is to observe the true contributions of an employee to a specific production function. Therefore, the principal-agent problem is worse than we think.

– Because the ability to search production function space increases with the number of people involved, “empire building” is a rational strategy for an employee to increase both his apparent and his actual value to the firm.

I think it’s probably safe to assume that all peaks are local. Some are just more local than others 🙂

But yes, large companies became large by finding a really high local peak that covered a lot of area in the fitness landscape. Startups can’t compete against the incumbent so they must look farther afield. A few of them may discover an even higher peak.